TY - JOUR
AU1 - Pham, Thang
AU2 - Vinh, Le
AU3 - de Zeeuw, Frank
AB - We determine which quadratic polynomials in three variables are expanders over an arbitrary field
$$\mathbb{F}$$
F
. More precisely, we prove that for a quadratic polynomial f ∈
$$\mathbb{F}$$
F
[x,y,z], which is not of the form g(h(x)+k(y)+l(z)), we have |f(A×B×C)|≫N
3/2 for any sets A,B,C ⊂
$$\mathbb{F}$$
F
with |A|=|B|=|C|=N, with N not too large compared to the characteristic of F.
TI - Three-Variable Expanding Polynomials and Higher-Dimensional Distinct Distances
JF - Combinatorica
DO - 10.1007/s00493-017-3773-y
DA - 2018-06-05
UR - https://www.deepdyve.com/lp/springer-journals/three-variable-expanding-polynomials-and-higher-dimensional-distinct-DuhfY84WEZ
SP - 411
EP - 426
VL - 39
IS - 2
DP - DeepDyve